Let’s get on the same page by calling up an accepted industry definition of Return Loss. (IEEE 1988) defines Return Loss as:

(1) (data transmission) (A) At a discontinuity in a transmission system the difference between the power incident upon the discontinuity. (B) The ratio in decibels of the power incident upon the discontinuity to the power reflected from the discontinuity. Note: This ratio is also the square of the reciprocal to the magnitude of the reflection coefficient. (C) More broadly, the return loss is a measure of the dissimilarity between two impedances, being equal to the number of decibels that corresponds to the scalar value of the reciprocal of the reflection coefficient, and hence being expressed by the following formula:

20*log

_{10}|(Z_{1}+Z_{2})/(Z_{1}-Z_{2})| decibelwhere Z

_{1}and Z_{2}= the two impedances.(2) (or gain) (waveguide). The ratio of incident to reflected power at a reference plane of a network.

A mathematically equivalent expression is that \(ReturnLoss=\frac{P_{incident}}{P_{reflected}}=\frac{P_{fwd}}{P_{rev}}\).

ReturnLoss is fundamentally a power ratio that can be expressed in dB. This article uses ReturnLoss as simply a power ratio.

## Return Loss Bridge (RLB)

A Return Loss Bridge (RLB) is a common implementation of a Directional Coupler, a device that can in a given transmission lines context (meaning wrt some given characteristic impedance Zref), be used to measure forward wave to reverse wave components and calculate their ratio, ie the ReturnLoss.

Let’s look at the common resistive RLB in detail.

Above is an LTSPICE model of an ideal RLB and source with Zref=50+j0Ω. Note:

- ALL the resistors (except for the unknown Zu) are equal to Zref;
- I1 and R3 model an ideal source with Zs=Zref; and
- R13 is the ‘floating’ measurement detector, again it presents a load of Zref.

Let’s explore some interesting properties of this ideal RLB.

Above are measurements of V(a)-V(b) for short circuit (sc) Zu and open circuit (oc) Zu.

Note that the magnitude of V(a)-V(b) is exactly the same for the sc case as for the oc case, but the polarity is opposite.

Also reported above is:

- the voltage Voc across Zu for oc; and
- the current Isc through Zu for sc.

From these we can calculate a Thevenin equivalent looking into the Zu terminals, it is Vth=25V and Rth=50Ω.

Rth is a very important property, for an ideal RLB, it presents a Thevenin source impedance equal to the design impedance Zref. If this does not match the measurement context, then error may be introduced.

### A measurement procedure

To use an RLB to measure ReturnLoss of some Zu, a matched generator is connected to the bridge, a matched detector connected to the bridge. The detector is then read with an oc or sc on the Zu port and the magnitude V1 written down (it should be the same for either oc or sc). The unknown is then connected and detector magnitude written Vu down. \(ReturnLoss=(\frac{V_1}{V_u})^2\). The magnitude of the complex reflection coefficient \(\rho=\frac{V_u}{V_1}\).

If you measure the detector voltages as complex quantities, Vo=oc voltage, the complex reflection coefficient \(\Gamma=\frac{V_u}{V_o}\).

### LTSPICE model results

Above is a table of results for three different Zu. Gamma (or s11) is calculated by dividing the detector voltage V(a)-V(b) by that measured for Zu=oc (Gamma=1).

Note that because everything is resistive in the model and it is DC excitation, all values above are purely real… but it works with AC and complex values though you will need a phase reference.

## Key properties of the ideal RLB

- The unknown port has a Thevenin equivalent source impedance of Zref;
- ReturnLoss and Gamma are measured wrt Zref;
- \(ReturnLoss=(\frac{|V_o|}{|V_u|})^2=(\frac{|V_s|}{|V_u|})^2\)
- \(\Gamma=\frac{V_u}{V_o}=\frac{V_u}{-V_s}\); and
- \(\rho=|\Gamma|=\frac{|V_u|}{|V_o|}=\frac{|V_u|}{|V_s|}\).

## Essential requirements of a good resistive RLB

- The source has a Thevenin equivalent source impedance of almost exactly Zref;
- three of the bridge resistors are almost exactly Zref; and
- the detector is a two terminal load almost perfectly isolated from ‘ground’ and has an impedance of almost exactly Zref.

## A RLB is not just a null indicator

Most ham RLB designs lack some of the essential requirements to permit it being used to measure ReturnLoss, though they may correctly null on the reference load.

Above is a table of ‘measurements’ from the ideal model in yellow, and calculated values. All of these columns are accurate only when the RLB meets the stated essential requirements.

# Links / References

- Bird, Trevor. April 2009a. Definition and Misuse of Return Loss. IEEE Antennas & Propagation Magazine, vol.51, iss.2, pp.166-167, April 2009.
- ———. April 2009b. Definition and Misuse of Return Loss. http://ieeeaps.org/aps_trans/docs/ReturnLossAPMag_09.pdf. (accessed 06/09/11).
- IEEE. 1988. IEEE standard dictionary of electrical and electronic terms, IEEE Press, 4th Edition, 1988.